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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Natural extensions for the Rosen fractions


Authors: Robert M. Burton, Cornelis Kraaikamp and Thomas A. Schmidt
Journal: Trans. Amer. Math. Soc. 352 (2000), 1277-1298
MSC (2000): Primary 11J70, 37A25
Published electronically: October 15, 1999
MathSciNet review: 1650073
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Abstract: The Rosen fractions form an infinite family which generalizes the nearest-integer continued fractions. We find planar natural extensions for the associated interval maps. This allows us to easily prove that the interval maps are weak Bernoulli, as well as to unify and generalize results of Diophantine approximation from the literature.


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Additional Information

Robert M. Burton
Affiliation: Department of Mathematics, Oregon State University, Corvallis, Oregon 97331
Email: burton@math.orst.edu

Cornelis Kraaikamp
Affiliation: Technische Universiteit Delft & Thomas Stieltjes Institute of Mathematics, ITS (SSOR), Mekelweg 4, 2628 CD Delft, the Netherlands
Email: c.kraaikamp@its.tudelft.nl

Thomas A. Schmidt
Affiliation: Department of Mathematics, Oregon State University, Corvallis, Oregon 97331
Email: toms@math.orst.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02442-3
PII: S 0002-9947(99)02442-3
Received by editor(s): August 1, 1997
Published electronically: October 15, 1999
Additional Notes: The first author was partially supported by AFOSR grant 93-1-0275 and NSF grant DMS 96-26575. The third author was partially supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)
Article copyright: © Copyright 1999 American Mathematical Society